I understand different exercises are used if the spine has too much motion versus too little motion. Is it possible to have both problems at the same time?

Yes, definitely. The spine is made up of many individual units. There can be differences in the amount of motion from one segment to another.

Sometimes a spinal joint or segment with decreased motion will cause the level above or the level below to make up the difference. One or both of the adjacent levels can become hypermobile (too much motion).

This is why osteopaths, chiropractors, and physical therapists who treat the spine usually test for motion at the painful level, above, and below. Treatment may start with one segment and move to the next as the spine adapts and shifts back to normal.